Fostering Exemplary Mathematics Teaching and Learning in Your School Sheryl Stump, Ball State University Angela Snyder, Carmel Clay Schools

Goals At the end of the session, participants will be able to identify and describe: What to look for in the K-12 mathematics classroom. How to support teachers in refining their teaching practices.

A Peek into One Mathematics Classroom

Shamrock Smile Mile Put checks beside any of the representations that are accurate for our problem of 2/3 of 3/4. Select any 2 of the representations and write an explanation for why it is accurate or why it is not an accurate representation.

A Passion for Fractions Lesson Objective: Multiply a fraction by a fraction Becky Pittard Pathways Elementary School Ormond Beach, FL 5th Grade

What did you notice in the video?

What to Look for in the K-12 Mathematics Classroom Effective Mathematics Teaching Practices & Classroom Norms

Effective Mathematics Teaching Practices Establish mathematics goals to focus learning. Effective teaching of mathematics establishes clear goals for the mathematics that students are learning, situates goals within learning progressions, and uses the goals to guide instructional decisions. Implement tasks that promote reasoning and problem solving. Effective teaching of mathematics engages students in solving and discussing tasks that promote mathematical reasoning and problem solving and allow multiple entry points and varied solution strategies. Use and connect mathematical representations. Effective teaching of mathematics engages students in making connections among mathematical representations to deepen understanding of mathematics concepts and procedures and as tools for problem solving. Facilitate meaningful mathematical discourse. Effective teaching of mathematics facilitates discourse among students to build shared understanding of mathematical ideas by analyzing and comparing student approaches and arguments. Pose purposeful questions. Effective teaching of mathematics uses purposeful questions to assess and advance students’ reasoning and sense making about important mathematical ideas and relationships. Build procedural fluency from conceptual understanding. Effective teaching of mathematics builds fluency with procedures on a foundation of conceptual understanding so that students, over time, become skillful in using procedures flexibly as they solve contextual and mathematical problems. Support productive struggle in learning mathematics. Effective teaching of mathematics consistently provides students, individually and collectively, with opportunities and supports to engage in productive struggle as they grapple with mathematical ideas and relationships. Elicit and use evidence of student thinking. Effective teaching of mathematics uses evidence of student thinking to assess progress toward mathematical understanding and to adjust instruction continually in ways that support and extend learning. Handout Read and underline important phrases. Turn to your Handout. Read and underline important phrases. Then turn and share one important idea that stood out for you with a neighbor. Allow about 7 minutes.

mathematical representations. Use and connect mathematical representations. Math Teaching Practice 3 Strengthening the ability to move between and among these representations improves the growth of children’s concepts. (Lesh, Post, & Behr, 1997)

mathematical representations Use and connect mathematical representations Different representations should: Be introduced, discussed, and connected. Focus students’ attention on the structure of mathematical ideas by examining essential features. Support students’ ability to justify and explain their reasoning. (Lesh, Post, & Behr, 1987; Marshall, Superfine, & Canty, 2010; Tripathi, 2008; Webb, Boswinkel, & Dekker, 2008)

Use and Connect Mathematical Representations: Teacher and Student Actions

Facilitate meaningful mathematical discourse. Teaching Practice 4 Discussions that focus on cognitively challenging mathematical tasks, namely those that promote thinking, reasoning, and problem solving, are a primary mechanism for promoting conceptual understanding of mathematics. (Hatano & Inagaki 1991; Michaels, O’Connor, & Resnick 2008)

Facilitate meaningful mathematical discourse Mathematical discourse should: Build on and honor students’ thinking. Let students share ideas, clarify understandings, and develop convincing arguments. Engage students in analyzing and comparing varied student approaches and strategies. Advance the math learning of the whole class. (Carpenter, Franke, & Levi, 2003; Fuson & Sherin, 2014; Smith & Stein, 2011)

Facilitate Meaningful Discourse: Teacher and Student Actions

Pose purposeful questions. Math Teaching Practice 5 Teachers’ questions are crucial in helping students make connections and learn important mathematics concepts. (Weiss & Pasley, 2004)

Pose purposeful questions Effective Questions should: Reveal students’ current understandings. Encourage students to explain, elaborate, or clarify their thinking. Make the targeted mathematical ideas more visible and accessible for student examination and discussion. (Boaler & Brodie, 2004; Chapin & O’Connor, 2007; Herbel-Eisenmann & Breyfogle, 2005)

Pose Purposeful Questions: Teacher and Student Actions

Build procedural fluency from conceptual understanding. Math Teaching Practice 6 Build procedural fluency from conceptual understanding. A rush to fluency undermines students’ confidence and interest in mathematics and is considered a cause of mathematics anxiety. (Ashcraft 2002; Ramirez Gunderson, Levine, & Beilock, 2013)

Build procedural fluency from conceptual understanding Procedural Fluency should: Build on a foundation of conceptual understanding. Over time (months, years), result in known facts and generalized methods for solving problems. Enable students to flexibly choose among methods to solve contextual and mathematical problems. (Baroody, 2006; Fuson & Beckmann, 2012/2013; Fuson, Kalchman, & Bransford, 2005; Russell, 2006)

Fluency develops over time... and it builds from conceptual understanding. Initial exploration and discussion Informal reasoning strategies Eventual use of general methods Principles to Actions (NCTM, 2014, p. 42)

Build Procedural Fluency from Conceptual Understanding: Teacher and Student Actions

Support productive struggle in learning mathematics. Teaching Practice 7 Support productive struggle in learning mathematics. The struggle we have in mind comes from solving problems that are within reach and grappling with key mathematical ideas that are comprehendible but not yet well formed. (Hiebert, Carpenter, Fennema, Fuson, Human, Murray, Olivier, & Wearne, 1996)

Support productive struggle in learning mathematics Productive Struggle should: Be considered essential to learning mathematics with understanding. Develop students’ capacity to persevere in the face of challenge. Help students realize that they are capable of doing well in mathematics with effort in using appropriate strategies. (Black, Trzesniewski, & Dweck, 2007; Dweck, 2008; Hiebert & Grouws, 2007; Kapur, 2010; Warshauer, 2011)

Support Productive Struggle in Learning Mathematics: Teacher and Student Actions

Tool 2.8 Effective Teaching “Look-Fors”

Classroom Norms

How to Support Teachers in Refining their Teaching Practices Coaching-Cycle Tools & Mathematics Teacher Leadership

Coaching-Cycle Tools Planning Data-Gathering Reflection

4.3 Planning Tool: Building Perseverance

4.6 Data-Gathering Tool: Building Perseverance

4.11 Reflection Tool: Building Perseverance

Mathematics Teacher Leadership Mathematics teacher leaders are school-based teacher leaders who are responsible for supporting other teachers with mathematics teaching and learning.

Some Options for Mathematics Teacher Leadership Team Learning Individual LEARNING Grade-Level Collaborative Planning Analyzing Student Work Lesson Study Lesson Design Instructional Rounds Assessment Development Engaging in Mathematics Demonstration Lessons Co-Planning and Co-Teaching Collaborative Coaching Pre-Observation Discussion Observation Post-Observation Discussion

Upcoming Events HAMTE Mathematics Teacher Leadership Conference & Indiana Mathematics Leadership Academy

HAMTE Mathematics Teacher Leadership Conference Friday, March 9, 2018, 8:30 am – 3:30 pm Schwitzer Student Center, University of Indianapolis Keynote speakers Shannon Larsen and Jenny Jorgensen, from the University of Maine, provide expertise in mathematics coaching Morning and afternoon breakout sessions focus on specific issues related to mathematics teacher leadership in elementary and middle schools $40 per participant if registration completed by February 23 Conference website: https://hamte.wildapricot.org/events

Indiana Mathematics Leadership Academy

Teams of Grades K-8 principals & teacher leaders will — Establish a clear and common vision for mathematics teaching learning in their schools. Develop knowledge and use tools for supporting effective mathematics teaching and visionary professional learning. Work collaboratively to develop and implement plans for activating their common vision.

Indiana Mathematics Leadership Academy Summer Institute Follow-Up Seminars June 12-14, 2018 Plconnect.info/IMLA October 3, 2018 February 6, 2019 April 10, 2019 $200/participant